Question

plz help me plz plz plz it's very urgent.......

Answer 1

In triangle ADE and ABC
angle A = angle A
angleD= angle B(because DE//BC)
angleE=angle C

therefore the triangles are similar by AAA similarity criteria.

thus
AD/AE=AE/AC
AD/AD+BD=AE/EC+AE
2/7=3/3+EC
3+EC=3*7/2=21/2=10.5
EC=10.5-3=7.5
thus
EC =7.5cm

Answer 2

Give that DE is // to BC

⇒ ΔADE is similar to ΔABC

Find AC:

By property of similar triangle:

$\dfrac{AD}{AE} = \dfrac{AE}{AC}$

$\dfrac{2}{5 + 2} = \dfrac{3}{AC}$

$\dfrac{2}{7} = \dfrac{3}{AC}$

$2AC = 21$

$AC = 10.5$

Find EC:

AC = AE + EC

10.5 = 3 + EC

EC = 10.5 - 3

EC = 7.5 cm

Answer: EC is 7.5 cm